163,947 research outputs found
Novel Magnetic Quantization of sp Bonding in Monolayer Tinene
A generalized tight-binding model, which is based on the subenvelope
functions of the different sublattices, is developed to explore the novel
magnetic quantization in monolayer gray tin. The effects due to the
bonding, the spin-orbital coupling, the magnetic field and the electric field
are simultaneously taken into consideration. The unique magneto-electronic
properties lie in two groups of low-lying Landau levels, with different orbital
components, localization centers, state degeneracy, spin configurations, and
magnetic- and electric-field dependences. The first and second groups mainly
come from the and (,) orbitals, respectively. Their
Landau-level splittings are, respectively, induced by the electric field and
spin-orbital interactions. The intragroup anti-crossings are only revealed in
the former. The unique tinene Landau levels are absent in graphene, silicene
and germanene.Comment: 6 figure
A lower bound on the fidelity between two states in terms of their Bures distance
Fidelity is a fundamental and ubiquitous concept in quantum information
theory. Fuchs-van de Graaf's inequalities deal with bounding fidelity from
above and below. In this paper, we give a lower bound on the quantum fidelity
between two states in terms of their Bures distance.Comment: 5 pages, LaTeX, we have corrected some errors appearing in the
original manuscript. We have partially fixed the gap in the proof of the
previous versions. A new method towards the conjectured inequality in the
present version is being expecte
Multi-View Spectral Clustering via Structured Low-Rank Matrix Factorization
Multi-view data clustering attracts more attention than their single view
counterparts due to the fact that leveraging multiple independent and
complementary information from multi-view feature spaces outperforms the single
one. Multi-view Spectral Clustering aims at yielding the data partition
agreement over their local manifold structures by seeking
eigenvalue-eigenvector decompositions. However, as we observed, such classical
paradigm still suffers from (1) overlooking the flexible local manifold
structure, caused by (2) enforcing the low-rank data correlation agreement
among all views; worse still, (3) LRR is not intuitively flexible to capture
the latent data clustering structures. In this paper, we present the structured
LRR by factorizing into the latent low-dimensional data-cluster
representations, which characterize the data clustering structure for each
view. Upon such representation, (b) the laplacian regularizer is imposed to be
capable of preserving the flexible local manifold structure for each view. (c)
We present an iterative multi-view agreement strategy by minimizing the
divergence objective among all factorized latent data-cluster representations
during each iteration of optimization process, where such latent representation
from each view serves to regulate those from other views, such intuitive
process iteratively coordinates all views to be agreeable. (d) We remark that
such data-cluster representation can flexibly encode the data clustering
structure from any view with adaptive input cluster number. To this end, (e) a
novel non-convex objective function is proposed via the efficient alternating
minimization strategy. The complexity analysis are also presented. The
extensive experiments conducted against the real-world multi-view datasets
demonstrate the superiority over state-of-the-arts.Comment: Accepted to appear at IEEE Trans on Neural Networks and Learning
System
Complete permutation polynomials induced from complete permutations of subfields
We propose several techniques to construct complete permutation polynomials
of finite fields by virtue of complete permutations of subfields. In some
special cases, any complete permutation polynomials over a finite field can be
used to construct complete permutations of certain extension fields with these
techniques. The results generalize some recent work of several authors
A Survey of Dynamical Matrices Theory
In this note, we survey some elementary theorems and proofs concerning
dynamical matrices theory. Some mathematical concepts and results involved in
quantum information theory are reviewed. A little new result on the matrix
representation of quantum operation are obtained. And best separable
approximation for quantum operations is presented.Comment: 22 pages, LaTe
New constructions of quaternary bent functions
In this paper, a new construction of quaternary bent functions from
quaternary quadratic forms over Galois rings of characteristic 4 is proposed.
Based on this construction, several new classes of quaternary bent functions
are obtained, and as a consequence, several new classes of quadratic binary
bent and semi-bent functions in polynomial forms are derived. This work
generalizes the recent work of N. Li, X. Tang and T. Helleseth
Beyond Low-Rank Representations: Orthogonal Clustering Basis Reconstruction with Optimized Graph Structure for Multi-view Spectral Clustering
Low-Rank Representation (LRR) is arguably one of the most powerful paradigms
for Multi-view spectral clustering, which elegantly encodes the multi-view
local graph/manifold structures into an intrinsic low-rank self-expressive data
similarity embedded in high-dimensional space, to yield a better graph
partition than their single-view counterparts. In this paper we revisit it with
a fundamentally different perspective by discovering LRR as essentially a
latent clustered orthogonal projection based representation winged with an
optimized local graph structure for spectral clustering; each column of the
representation is fundamentally a cluster basis orthogonal to others to
indicate its members, which intuitively projects the view-specific feature
representation to be the one spanned by all orthogonal basis to characterize
the cluster structures. Upon this finding, we propose our technique with the
followings: (1) We decompose LRR into latent clustered orthogonal
representation via low-rank matrix factorization, to encode the more flexible
cluster structures than LRR over primal data objects; (2) We convert the
problem of LRR into that of simultaneously learning orthogonal clustered
representation and optimized local graph structure for each view; (3) The
learned orthogonal clustered representations and local graph structures enjoy
the same magnitude for multi-view, so that the ideal multi-view consensus can
be readily achieved. The experiments over multi-view datasets validate its
superiority.Comment: Accepted to appear in Neural Networks, Elsevier, on 9th March 201
Privacy Preserving Controller Synthesis via Belief Abstraction
Privacy is a crucial concern in many systems in addition to their given
tasks. We consider a new notion of privacy based on beliefs of the system
states, which is closely related to opacity in discrete event systems. To
guarantee the privacy requirement, we propose to abstract the belief space
whose dynamics is shown to be mixed monotone where efficient abstraction
algorithm exists. Based on the abstraction, we propose two different approaches
to synthesize controllers of the system to preserve privacy with an
illustrative example
On constructing complete permutation polynomials over finite fields of even characteristic
In this paper, a construction of complete permutation polynomials over finite
fields of even characteristic proposed by Tu et al. recently is generalized in
a recursive manner. Besides, several classes of complete permutation
polynomials are derived by computing compositional inverses of known ones.Comment: Stupid mistakes in previous versions are correcte
A lower bound of quantum conditional mutual information
In this paper, a lower bound of quantum conditional mutual information is
obtained by employing the Peierls-Bogoliubov inequality and Golden Thompson
inequality. Comparison with the bounds obtained by other researchers indicates
that our result is independent of any measurements. It may give some new
insights over squashed entanglement and perturbations of Markov chain states.Comment: 11 pages, LaTeX, published version. The missed second author is also
adde
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